Magnetic quantum ring in two-dimensional topological insulators

Highlights: • Inhomogeneous fields lead to in-gap magnetic edge states in topological insulators. • The band inversion can manifest itself through the magnetic edge states. • The snake-like states merge into the Landau levels by a special quantization rule. -- Abstract: The quantum properties of topological insulator magnetic quantum rings formed by inhomogeneous magnetic fields are investigated using a series expansion method for the modified Dirac equation. Cycloid-like and snake-like magnetic edge states are respectively found in the bulk gap for the normal and inverted magnetic field profiles. The energy spectra, current densities and classical trajectories of the magnetic edge states are discussed in detail. The bulk band inversion is found to manifest itself through the angular momentum transition in the ground state for the cycloid-like states and the resonance tunneling effect for the snake-like states.